Multiple imputation in the presence of non‐normal data

Multiple imputation (MI) is becoming increasingly popular for handling missing data. Standard approaches for MI assume normality for continuous variables (conditionally on the other variables in the imputation model). However, it is unclear how to impute non‐normally distributed continuous variables. Using simulation and a case study, we compared various transformations applied prior to imputation, including a novel non‐parametric transformation, to imputation on the raw scale and using predictive mean matching (PMM) when imputing non‐normal data. We generated data from a range of non‐normal distributions, and set 50% to missing completely at random or missing at random. We then imputed missing values on the raw scale, following a zero‐skewness log, Box–Cox or non‐parametric transformation and using PMM with both type 1 and 2 matching. We compared inferences regarding the marginal mean of the incomplete variable and the association with a fully observed outcome. We also compared results from these approaches in the analysis of depression and anxiety symptoms in parents of very preterm compared with term‐born infants. The results provide novel empirical evidence that the decision regarding how to impute a non‐normal variable should be based on the nature of the relationship between the variables of interest. If the relationship is linear in the untransformed scale, transformation can introduce bias irrespective of the transformation used. However, if the relationship is non‐linear, it may be important to transform the variable to accurately capture this relationship. A useful alternative is to impute the variable using PMM with type 1 matching. Copyright © 2016 John Wiley & Sons, Ltd.     

Reference‐based multiple imputation for missing data sensitivity analyses in trial‐based cost‐effectiveness analysis

Missing data are a common issue in cost‐effectiveness analysis (CEA) alongside randomised trials and are often addressed assuming the data are ‘missing at random’. However, this assumption is often questionable, and sensitivity analyses are required to assess the implications of departures from missing at random. Reference‐based multiple imputation provides an attractive approach for conducting such sensitivity analyses, because missing data assumptions are framed in an intuitive way by making reference to other trial arms. For example, a plausible not at random mechanism in a placebo‐controlled trial would be to assume that participants in the experimental arm who dropped out stop taking their treatment and have similar outcomes to those in the placebo arm. Drawing on the increasing use of this approach in other areas, this paper aims to extend and illustrate the reference‐based multiple imputation approach in CEA. It introduces the principles of reference‐based imputation and proposes an extension to the CEA context. The method is illustrated in the CEA of the CoBalT trial evaluating cognitive behavioural therapy for treatment‐resistant depression. Stata code is provided. We find that reference‐based multiple imputation provides a relevant and accessible framework for assessing the robustness of CEA conclusions to different missing data assumptions.     

Multiple imputation for harmonizing longitudinal non‐commensurate measures in individual participant data meta‐analysis

There are many advantages to individual participant data meta‐analysis for combining data from multiple studies. These advantages include greater power to detect effects, increased sample heterogeneity, and the ability to perform more sophisticated analyses than meta‐analyses that rely on published results. However, a fundamental challenge is that it is unlikely that variables of interest are measured the same way in all of the studies to be combined. We propose that this situation can be viewed as a missing data problem in which some outcomes are entirely missing within some trials and use multiple imputation to fill in missing measurements. We apply our method to five longitudinal adolescent depression trials where four studies used one depression measure and the fifth study used a different depression measure. None of the five studies contained both depression measures. We describe a multiple imputation approach for filling in missing depression measures that makes use of external calibration studies in which both depression measures were used. We discuss some practical issues in developing the imputation model including taking into account treatment group and study. We present diagnostics for checking the fit of the imputation model and investigate whether external information is appropriately incorporated into the imputed values. Copyright © 2015 John Wiley & Sons, Ltd.     

Funnel plots for population‐based cancer survival: principles,methods and applications

Funnel plots are graphical tools designed to detect excessive variation in performance indicators by simple visual inspection of the data. Their main use in the biomedical domain so far has been to detect publication bias in meta‐analyses, but they have also been recommended as the most appropriate way to display performance indicators for a vast range of health‐related outcomes. Here, we extend the use of funnel plots to population‐based cancer survival and several related measures. We present three applications to familiarise the reader with their interpretation. We propose funnel plots for various cancer survival measures, as well as age‐standardised survival, trends in survival and excess hazard ratios. We describe the components of a funnel plot and the formulae for the construction of the control limits for each of these survival measures. We include three transformations to construct the control limits for the survival function: complementary log–log, logit and logarithmic transformations. We present applications of funnel plots to explore the following: (i) small‐area and temporal variation in cancer survival; (ii) racial and geographical variation in cancer survival; and (iii) geographical variation in the excess hazard of death. Funnel plots provide a simple and informative graphical tool to display geographical variation and trend in a range of cancer survival measures. We recommend their use as a routine instrument for cancer survival comparisons, to inform health policy makers in planning and assessing cancer policies. We advocate the use of the complementary log–log or logit transformation to construct the control limits for the survival function. Copyright © 2013 John Wiley & Sons, Ltd.     

Missing data in trial‐based cost‐effectiveness analysis: An incomplete journey

Cost‐effectiveness analyses (CEA) conducted alongside randomised trials provide key evidence for informing healthcare decision making, but missing data pose substantive challenges. Recently, there have been a number of developments in methods and guidelines addressing missing data in trials. However, it is unclear whether these developments have permeated CEA practice. This paper critically reviews the extent of and methods used to address missing data in recently published trial‐based CEA. Issues of the Health Technology Assessment journal from 2013 to 2015 were searched. Fifty‐two eligible studies were identified. Missing data were very common; the median proportion of trial participants with complete cost‐effectiveness data was 63% (interquartile range: 47%–81%). The most common approach for the primary analysis was to restrict analysis to those with complete data (43%), followed by multiple imputation (30%). Half of the studies conducted some sort of sensitivity analyses, but only 2 (4%) considered possible departures from the missing‐at‐random assumption. Further improvements are needed to address missing data in cost‐effectiveness analyses conducted alongside randomised trials. These should focus on limiting the extent of missing data, choosing an appropriate method for the primary analysis that is valid under contextually plausible assumptions, and conducting sensitivity analyses to departures from the missing‐at‐random assumption.     

Sensitivity analysis for a partially missing binary outcome in a two‐arm randomized clinical trial

Although recent guidelines for dealing with missing data emphasize the need for sensitivity analyses, and such analyses have a long history in statistics, universal recommendations for conducting and displaying these analyses are scarce. We propose graphical displays that help formalize and visualize the results of sensitivity analyses, building upon the idea of ‘tipping‐point’ analysis for randomized experiments with a binary outcome and a dichotomous treatment. The resulting ‘enhanced tipping‐point displays’ are convenient summaries of conclusions obtained from making different modeling assumptions about missingness mechanisms. The primary goal of the displays is to make formal sensitivity analysesmore comprehensible to practitioners, thereby helping them assess the robustness of the experiment's conclusions to plausible missingness mechanisms. We also present a recent example of these enhanced displays in amedical device clinical trial that helped lead to FDA approval. Copyright © 2014 John Wiley & Sons, Ltd.     

Attitudes and beliefs of non‐participants in a population‐based screening programme for colorectal cancer

Background

Uptake of colorectal cancer screening programmes needs to be improved or at least maintained in order to achieve projected reductions in mortality and morbidity. Understanding the origins of non‐participation in screening is therefore important.

Objective

To explore the beliefs and experiences of individuals who had not responded either to their screening invitation or reminder.

Design

A qualitative study using in‐depth interviews with non‐participants from England''s population‐based colorectal cancer screening programme. Data collection and analysis were carried out using a grounded theory approach, with an emphasis on the constant comparison method, and continued until saturation (27 interviews).

Findings

The interviews provided an in‐depth understanding of a range of reasons and circumstances surrounding non‐participation in screening, including contextual and environmental influences as well as factors specific to the screening test. Non‐participation in screening was not necessarily associated with negative attitudes towards screening or a decision to not return a kit. Reasons for non‐participation in screening included not feeling that participation is personally necessary, avoiding or delaying decision making, and having some degree of intention to take part but failing to do so because of practicalities, conflicting priorities or external circumstances. Beliefs, awareness and intention change over time.

Discussion and conclusions

A range of approaches may be required to improve screening uptake. Some non‐participants may already have a degree of intention to take part in screening in the future, and this group may be more responsive to interventions based on professional endorsement, repeat invitations, reminders and aids to making the test more practical.     

Imputation of systematically missing predictors in an individual participant data meta‐analysis: a generalized approach using MICE

Individual participant data meta‐analyses (IPD‐MA) are increasingly used for developing and validating multivariable (diagnostic or prognostic) risk prediction models. Unfortunately, some predictors or even outcomes may not have been measured in each study and are thus systematically missing in some individual studies of the IPD‐MA. As a consequence, it is no longer possible to evaluate between‐study heterogeneity and to estimate study‐specific predictor effects, or to include all individual studies, which severely hampers the development and validation of prediction models. Here, we describe a novel approach for imputing systematically missing data and adopt a generalized linear mixed model to allow for between‐study heterogeneity. This approach can be viewed as an extension of Resche‐Rigon's method (Stat Med 2013), relaxing their assumptions regarding variance components and allowing imputation of linear and nonlinear predictors. We illustrate our approach using a case study with IPD‐MA of 13 studies to develop and validate a diagnostic prediction model for the presence of deep venous thrombosis. We compare the results after applying four methods for dealing with systematically missing predictors in one or more individual studies: complete case analysis where studies with systematically missing predictors are removed, traditional multiple imputation ignoring heterogeneity across studies, stratified multiple imputation accounting for heterogeneity in predictor prevalence, and multilevel multiple imputation (MLMI) fully accounting for between‐study heterogeneity. We conclude that MLMI may substantially improve the estimation of between‐study heterogeneity parameters and allow for imputation of systematically missing predictors in IPD‐MA aimed at the development and validation of prediction models. Copyright © 2015 John Wiley & Sons, Ltd.     

Epidemiology of sepsis in cancer patients in Victoria,Australia: a population‐based study using linked data

Objective : To determine the clinical characteristics, outcomes and longitudinal trends of sepsis occurring in cancer patients. Method : Retrospective study using statewide Victorian Cancer Registry data linked to various administrative datasets. Results : Among 215,763 incident cancer patients, incidence of sepsis within one year of cancer diagnosis was estimated at 6.4%. The incidence of sepsis was higher in men, younger patients, patients diagnosed with haematological malignancies and those with de novo metastatic disease. Of the 13,316 patients with a first admission with sepsis, 55% had one or more organ failures, 29% required care within an intensive care unit and 13% required mechanical ventilation. Treatments associated with the highest sepsis incidence were stem cell/bone marrow transplant (33%), major surgery (4.4%), chemotherapy (1.1%) and radical radiotherapy (0.6%). The incidence of sepsis with organ failure increased between 2008 and 2015, while 90‐day mortality decreased. Conclusions : Sepsis in patients with cancer has high mortality and occurs most frequently in the first year after cancer diagnosis. Implications for public health : The number of cancer patients diagnosed with sepsis is expected to increase, causing a substantial burden on patients and the healthcare system.     

Improving on analyses of self‐reported data in a large‐scale health survey by using information from an examination‐based survey

Common data sources for assessing the health of a population of interest include large‐scale surveys based on interviews that often pose questions requiring a self‐report, such as, ‘Has a doctor or other health professional ever told you that you have 〈 health condition of interest〉 ?’ or ‘What is your 〈 height/weight〉 ?’ Answers to such questions might not always reflect the true prevalences of health conditions (for example, if a respondent misreports height/weight or does not have access to a doctor or other health professional). Such ‘measurement error’ in health data could affect inferences about measures of health and health disparities. Drawing on two surveys conducted by the National Center for Health Statistics, this paper describes an imputation‐based strategy for using clinical information from an examination‐based health survey to improve on analyses of self‐reported data in a larger interview‐based health survey. Models predicting clinical values from self‐reported values and covariates are fitted to data from the National Health and Nutrition Examination Survey (NHANES), which asks self‐report questions during an interview component and also obtains clinical measurements during a physical examination component. The fitted models are used to multiply impute clinical values for the National Health Interview Survey (NHIS), a larger survey that obtains data solely via interviews. Illustrations involving hypertension, diabetes, and obesity suggest that estimates of health measures based on the multiply imputed clinical values are different from those based on the NHIS self‐reported data alone and have smaller estimated standard errors than those based solely on the NHANES clinical data. The paper discusses the relationship of the methods used in the study to two‐phase/two‐stage/validation sampling and estimation, along with limitations, practical considerations, and areas for future research. Published in 2009 by John Wiley & Sons, Ltd.     

Multiple imputation for handling systematically missing confounders in meta‐analysis of individual participant data

A variable is ‘systematically missing’ if it is missing for all individuals within particular studies in an individual participant data meta‐analysis. When a systematically missing variable is a potential confounder in observational epidemiology, standard methods either fail to adjust the exposure–disease association for the potential confounder or exclude studies where it is missing. We propose a new approach to adjust for systematically missing confounders based on multiple imputation by chained equations. Systematically missing data are imputed via multilevel regression models that allow for heterogeneity between studies. A simulation study compares various choices of imputation model. An illustration is given using data from eight studies estimating the association between carotid intima media thickness and subsequent risk of cardiovascular events. Results are compared with standard methods and also with an extension of a published method that exploits the relationship between fully adjusted and partially adjusted estimated effects through a multivariate random effects meta‐analysis model. We conclude that multiple imputation provides a practicable approach that can handle arbitrary patterns of systematic missingness. Bias is reduced by including sufficient between‐study random effects in the imputation model. Copyright © 2013 John Wiley & Sons, Ltd.     

Missing values in longitudinal dietary data: A multiple imputation approach based on a fully conditional specification

Multiple imputation (MI) has increasingly received attention as a flexible tool to resolve missing data problems both in observational and controlled studies. Our goal has been to develop a valid and efficient MI procedure for the Diabetes Prediction and Prevention Nutrition Study, in which the diet of a cohort of newborn children with HLA‐DQB1‐conferred susceptibility to type 1 diabetes is repeatedly measured by 3‐day food records over early childhood. The estimation of risk is based on a nested case‐control design setup within the cohort. We have used an iterative procedure known as the fully conditional specification (FCS) to generate appropriate values for the missing dietary data, here playing the role of time‐dependent covariates. Our method extends the standard FCS to repeated measurements settings with the possibility of non‐monotone missingness patterns by being doubly iterative over the follow‐up time of the individuals. In addition, our proposed procedure is nonparametric in the sense that the variables can have distributions deviating strongly from normality: it makes use of quantile normal scores to transform to normality, performs imputations, and transforms back to the original scale. By the use of a moving time window and stepwise regression procedures, the two‐fold FCS method operates well with a great number of variables each measured repeatedly over time. Extensive simulation studies demonstrate that the procedure together with the proposed transformations and variable selection methods provides tools for valid and efficient statistical inference in the nested case‐control setting, and its applications extend beyond that. Copyright © 2009 John Wiley & Sons, Ltd.     

Addressing Missing Data in Patient‐Reported Outcome Measures (PROMS): Implications for the Use of PROMS for Comparing Provider Performance

Patient‐reported outcome measures (PROMs) are now routinely collected in the English National Health Service and used to compare and reward hospital performance within a high‐powered pay‐for‐performance scheme. However, PROMs are prone to missing data. For example, hospitals often fail to administer the pre‐operative questionnaire at hospital admission, or patients may refuse to participate or fail to return their post‐operative questionnaire. A key concern with missing PROMs is that the individuals with complete information tend to be an unrepresentative sample of patients within each provider and inferences based on the complete cases will be misleading. This study proposes a strategy for addressing missing data in the English PROM survey using multiple imputation techniques and investigates its impact on assessing provider performance. We find that inferences about relative provider performance are sensitive to the assumptions made about the reasons for the missing data. © 2015 The Authors. Health Economics Published by John Wiley & Sons Ltd.     

Handling incomplete correlated continuous and binary outcomes in meta‐analysis of individual participant data

Meta‐analysis of individual participant data (IPD) is increasingly utilised to improve the estimation of treatment effects, particularly among different participant subgroups. An important concern in IPD meta‐analysis relates to partially or completely missing outcomes for some studies, a problem exacerbated when interest is on multiple discrete and continuous outcomes. When leveraging information from incomplete correlated outcomes across studies, the fully observed outcomes may provide important information about the incompleteness of the other outcomes. In this paper, we compare two models for handling incomplete continuous and binary outcomes in IPD meta‐analysis: a joint hierarchical model and a sequence of full conditional mixed models. We illustrate how these approaches incorporate the correlation across the multiple outcomes and the between‐study heterogeneity when addressing the missing data. Simulations characterise the performance of the methods across a range of scenarios which differ according to the proportion and type of missingness, strength of correlation between outcomes and the number of studies. The joint model provided confidence interval coverage consistently closer to nominal levels and lower mean squared error compared with the fully conditional approach across the scenarios considered. Methods are illustrated in a meta‐analysis of randomised controlled trials comparing the effectiveness of implantable cardioverter‐defibrillator devices alone to implantable cardioverter‐defibrillator combined with cardiac resynchronisation therapy for treating patients with chronic heart failure. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.